1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Simple Polynomial

  1. May 15, 2008 #1
    Help me to solve this simple problem
    find a if
    fx = 2x^3 - ax^2 + 2x - 7
    has a repeated factor
     
  2. jcsd
  3. May 15, 2008 #2
    Use a trial and error method. Find a value of 'x' that would make f(x)=0 for some value of 'a'. Hint: what's f(1), and what value of 'a' corresponds?
     
  4. May 15, 2008 #3
    any easier way? Because this is in Further math syllabus so trial and error method seems too long. Or can you show me BrendanH?
     
  5. May 15, 2008 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    If x0 is a double root and x1 is a different root, then your polynomial can be written 2(x- x0)2(x- x1). Multiply that out compare to the given polynomial.

    "Multiple root" might mean a triple root: 2(x- x0)3. Multiply that out and compare to the given polynomial.
     
  6. May 15, 2008 #5

    symbolipoint

    User Avatar
    Homework Helper
    Education Advisor
    Gold Member

    Have you tried Rational Roots Theorem and synthetic division? Picking rational roots to try will not immediately involve 'a'. The synthetic division will certainly involve 'a'. The use of synthetic division either gives remainder of zero for a root or a nonzero remainder if a choice is not a root.
     
  7. May 15, 2008 #6

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    The trouble with rational roots and factoring etc, is that the double root doesn't look like it's rational. Try this. If x is a double root then f(x)=0 and f'(x)=0. Solve those simultaneously. You wind up having to solve a cubic.
     
  8. May 15, 2008 #7
    What is repeated factor? Does it mean that it has two or more same roots? (Its translation problem)
     
  9. May 15, 2008 #8

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Yes, it has two or more of the same root.
     
  10. May 16, 2008 #9

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Why would you think that this equation will have a rational root?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Simple Polynomial
  1. On polynomials (Replies: 7)

  2. Simple polynomial (Replies: 3)

Loading...